Lifshitz Model Research Articles

Nonlinear dynamics of the semi-infinite ferromagnetic samples with an easy-plane anisotropy

The modification of the inverse scattering problem is proposed to investigate solitons and dispersive waves in the framework of the Landau–Lifshitz model for semi-infinite ferromagnet with an ¡¡easy-plane¿¿ anisotropy under the mixed boundary conditions, corresponding to different degrees of spin pinning on the edge of the sample. New types of solitons are obtained and their elastic reflection from the edge of the sample is analyzed. Spectral expansions of the integrals of motion for solitons and waves are found. Additional integrals of motion are established that guarantee true boundary conditions for solitons, when they interact with the edge of the sample.

Observational Constraints on the Parameters of Hořava–Lifshitz Gravity

AbstractThis study investigates the accelerated cosmic expansion within the Hořava–Lifshitz (HL) Model. To constrain the cosmological parameters of this model, 17 Baryon Acoustic Oscillation points, 31 Cosmic Chronometer points, 40 Type Ia Supernovae points, 24 quasar Hubble diagram points, and 162 Gamma Ray Bursts points, along with the latest Hubble constant measurement (R22) are incorporated. is treated as a free parameter to extract and using late‐time datasets, aiming for optimal fitting values in each model. Treating as free improves precision, reduces bias, and enhances dataset compatibility. The obtained values of and are compared to the model, showing consistency with previous estimates from Planck and SDSS studies. The Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) favor the Hořava–Lifshitz model, with the model having the lowest AIC. Additionally, and analyses are conducted to assess model preference. Validation using the reduced statistic indicates satisfactory fits for the Hořava–Lifshitz model, while recognizing as the preferred model. Extensions of the analysis warrant further investigation.

Gauge equivalence of $$1+1$$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model

Gauge equivalence of $$1+1$$ Calogero–Moser–Sutherland field theory and a higher-rank trigonometric Landau–Lifshitz model

Deconfinement Dynamics of Fractons in Tilted Bose-Hubbard Chains.

Fractonic constraints can lead to exotic properties of quantum many-body systems. Here, we investigate the dynamics of fracton excitations on top of the ground states of a one-dimensional, dipole-conserving Bose-Hubbard model. We show that nearby fractons undergo a collective motion mediated by exchanging virtual dipole excitations, which provides a powerful dynamical tool to characterize the underlying ground-state phases. We find that, in the gapped Mott insulating phase, fractons are confined to each other as motion requires the exchange of massive dipoles. When crossing the phase transition into a gapless Luttinger liquid of dipoles, fractons deconfine. Their transient deconfinement dynamics scales diffusively and exhibits strong but subleading contributions described by a quantum Lifshitz model. We examine prospects for the experimental realization in tilted Bose-Hubbard chains by numerically simulating the adiabatic state preparation and subsequent time evolution and find clear signatures of the low-energy fracton dynamics.

Lifshitz model in the presence of spin–orbit coupling

Wave function of a localized state created by a short-range impurity in two dimensions falls off with distance, r, from the impurity as 1r1/2exp(−ra), where a is the localization radius. With randomly positioned identical impurities with low concentration, n≪a−2, the level smears into a band due to the overlap of the impurity wave functions. This is the essence of the Lifshitz model. We demonstrate that, upon incorporation of the spin–orbit coupling, the impurity wave functions acquire oscillating factors which, subsequently, modify their overlap. As a result of such modification, the density of states develops singularities at certain energies.

Quantitative constraints on modified gravity paradigms

We use low-redshift background cosmology data to place quantitative constraints on three separate modified gravity models, each of which aims to explain the low-redshift acceleration through a different physical mechanism. The Lifshitz cosmology is effectively a parametric extension of the canonical $\Lambda$CDM model, where a time-dependent cosmological constant originates from vacuum energy. The Infinite Statistics model is also a parametric extension of $\Lambda$CDM, where the dark energy is dynamic and originates from the curvature of a dual space-time. We show that the data restricts the additional parameters in these models to be consistent with their $\Lambda$CDM values, and in particular that it implies that the theoretically predicted value for a dimensionless coupling parameter in the Lifshitz model is ruled out at more than six standard deviations. In the Regge-Teitelboim model, gravity is described by embedding the usual space-time manifold in a fixed higher-dimensional background, and there is no parametric $\Lambda$CDM limit. We study several separate realizations of the model, respectively introduced by Davidson, by Fabi \textit{et al.}, and by Stern \& Xu, and show that the first two are ruled out by the low-redshift data we use, while the latter is consistent with this data but requires a non-standard value of the matter density. Overall, our analysis highlights the tight constraints imposed by current data on the allowed low-redshift deviations from the standard $\Lambda$CDM background evolution.

Nonlinear Dynamics of a Heisenberg Ferromagnet on the Semiaxis

The nonlinear dynamics of a semi-infinite isotropic ferromagnet with partial spin pinning at the sample edge, as well as in the limiting cases of full spin pinning and in its absence, is investigated based on the Landau–Lifshitz model using the inverse scattering transform. Two types of solitons are predicted. The first of them represents magnetization oscillations with discrete frequencies, which are localized near the sample surface. The second type contains moving particle-like objects with deformable cores, which are elastically reflected from the sample boundary, whereas at large distances from the boundary they are transformed into the typical solitons of an extended ferromagnet. Peculiarities in collisions of solitons with the sample boundary are analyzed for various degrees of spin pinning on the surface. A set of new conservation laws is obtained, which guarantee the fulfillment of the required boundary conditions for solitons and ensure the localization of solitons near the sample surface or their reflection from it.

A zoo of deformed Jackiw-Teitelboim models near large dimensional black holes

We consider a charged Lifshitz black hole in the large transverse dimension limit. In this setup, the dynamics near the black hole horizon are shown to be effectively governed by a family of two-dimensional models of dilaton gravity depending on the ratio of the dynamical parameter characterizing the black hole and the dimension of spacetime. This family includes the Callan-Giddings-Harvey-Strominger (CGHS) and Jackiw-Teitelboim (JT) models and their charged equivalents. This family also contains classes of asymptotically anti-de Sitter models beyond JT, characterized by a running Ricci scalar, with the option of adding charge. Finally, we argue that specific non-minimally coupled probe scalars in the parent Lifshitz model become minimally coupled scalars in the two-dimensional theory, which is relevant for understanding semi-classical corrections in such models.

Periodic orbits in Hořava–Lifshitz cosmologies

We consider spatially homogeneous Hořava–Lifshitz models that perturb General Relativity (GR) by a parameter \(v\in (0,1)\) such that GR occurs at \(v=1/2\). We describe the dynamics for the extremal case \(v=0\), which possess the usual Bianchi hierarchy: type \(\textrm{I}\) (Kasner circle of equilibria), type \(\textrm{II}\) (heteroclinics that induce the Kasner map) and type \(\mathrm {VI_0},\mathrm {VII_0}\) (further heteroclinics). For type \(\textrm{VIII}\) and \(\textrm{IX}\), we use a computer-assisted approach to prove the existence of periodic orbits which are far from the Mixmaster attractor. Therefore we obtain a new behaviour which is not described by the BKL picture of bouncing Kasner-like states.

Lifshitz gauge duality

Motivated by variety of realizations of the compact Lifshitz model, I predict and explore properties of its three phases, study its phase transitions and derive its fractonic gauge dual. The resulting U(1) vector gauge theory efficiently and robustly encodes the restricted mobility of its dipole conserving charged matter and the corresponding topological vortex defects. The gauge theory provides a transparent formulation of the three phases of the Lifshitz model and gives a field theoretic formulation of the associated two-stage Higgs transitions.

Analysis of Landau–Lifshitz and neo-Hookean models for static and dynamic acoustoelastic testing

A comparison of three different isotropic non-linear elastic models uncovers subtle but important differences in the acoustoelastic responses of a material slab that is subjected to dynamic deformations during a pump-probe experiment. The probe wave deformations are small and are superimposed on larger underlying deformations using three different models: Landau–Lifshitz (using its fourth-order extension), compressible neo-Hookean model (properly accounting for volumetric deformations), and an alternative neo-Hookean model (fully decoupled energies due to distortional isochoric and volumetric deformations). The analyses yield elasticity tensors and respective expressions for the propagation speeds of P-wave and S-wave probes for each model. Despite having many similarities, the different models give different predictions of which probe wave types will have speeds that are perturbed by different pump wave types. The analyses also show a conceptual inconsistency in the Landau–Lifshitz model, that a simple shear deformation induces a stress and a shear wave probe speed that depend on the second-order elastic constant λ, which controls resistance to volumetric changes and thus should not be present in the expressions for shear stress and shear wave probe speeds. Thus, even though the Landau–Lifshitz model is widely used, it may not always be the best option to model experimental data.

Entanglement entropies of an interval in the free Schrödinger field theory on the half line

We study the entanglement entropies of an interval adjacent to the boundary of the half line for the free fermionic spinless Schrödinger field theory at finite density and zero temperature, with either Neumann or Dirichlet boundary conditions. They are finite functions of the dimensionless parameter given by the product of the Fermi momentum and the length of the interval. The entanglement entropy displays an oscillatory behaviour, differently from the case of the interval on the whole line. This behaviour is related to the Friedel oscillations of the mean particle density on the half line at the entangling point. We find analytic expressions for the expansions of the entanglement entropies in the regimes of small and large values of the dimensionless parameter. They display a remarkable agreement with the curves obtained numerically. The analysis is extended to a family of free fermionic Lifshitz models labelled by their integer Lifshitz exponent, whose parity determines the properties of the entanglement entropies. The cumulants of the local charge operator and the Schatten norms of the underlying kernels are also explored.

2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles

We compare the construction of 2D integrable models through two gauge field theories. The first one is the 4D Chern–Simons (4D-CS) theory proposed by Costello and Yamazaki. The second one is the 2D generalization of the Hitchin integrable systems constructed by means of affine Higgs bundles (AHB). We illustrate the latter approach by considering 1 + 1 field versions of integrable systems including the Calogero–Moser field theory, the Landau–Lifshitz model and the field theory generalization of the elliptic Gaudin model.

Entanglement entropies of an interval in the free Schrödinger field theory at finite density

We study the entanglement entropies of an interval on the infinite line in the free fermionic spinless Schrödinger field theory at finite density and zero temperature, which is a non-relativistic model with Lifshitz exponent z = 2. We prove that the entanglement entropies are finite functions of one dimensionless parameter proportional to the area of a rectangular region in the phase space determined by the Fermi momentum and the length of the interval. The entanglement entropy is a monotonically increasing function. By employing the properties of the prolate spheroidal wave functions of order zero or the asymptotic expansions of the tau function of the sine kernel, we find analytic expressions for the expansions of the entanglement entropies in the asymptotic regimes of small and large area of the rectangular region in the phase space. These expansions lead to prove that the analogue of the relativistic entropic C function is not monotonous. Extending our analyses to a class of free fermionic Lifshitz models labelled by their integer dynamical exponent z, we find that the parity of this exponent determines the properties of the bipartite entanglement for an interval on the line.

Characterization of ultra-intense laser in radiation damping regime using ponderomotive scattering

We present a novel approach to analyzing phase-space distributions of electrons ponderomotively scattered off an ultra-intense laser pulse and comment on the implications for the thus conceivable in-situ laser-characterization schemes. To this end, we present fully relativistic test particle simulations of electrons scattered from an ultra-intense, counter-propagating laser pulse. The simulations unveil non-trivial scalings of the scattered electron distribution with the laser intensity, pulse duration, beam waist, and energy of the electron bunch. We quantify the found scalings by means of an analytical expression for the scattering angle of an electron bunch ponderomotively scattered from a counter-propagating, ultra-intense laser pulse, also accounting for radiation reaction (RR) through the Landau–Lifshitz (LL) model. For various laser and bunch parameters, the derived formula is in excellent quantitative agreement with the simulations. We also demonstrate how, in the radiation-dominated regime, a simple re-scaling of our model’s input parameter yields quantitative agreement with numerical simulations based on the LL model.

Critical drag as a mechanism for resistivity

A quantum many-body system with a conserved electric charge can have a DC resistivity that is either exactly zero (implying it supports dissipationless current) or nonzero. Exactly zero resistivity is related to conservation laws that prevent the current from degrading. In this paper, we carefully examine the situations in which such a circumstance can occur. We find that exactly zero resistivity requires either continuous translation symmetry, or an internal symmetry that has a certain kind of "mixed anomaly" with the electric charge. (The symmetry could be a generalized global symmetry associated with the emergence of unbreakable loop or higher dimensional excitations.) However, even if one of these is satisfied, we show that there is still a mechanism to get nonzero resistivity, through critical fluctuations that drive the susceptibility of the conserved quantity to infinity; we call this mechanism "critical drag". Critical drag is thus a mechanism for resistivity that, unlike conventional mechanisms, is unrelated to broken symmetries. We furthermore argue that an emergent symmetry that has the appropriate mixed anomaly with electric charge is in fact an inevitable consequence of compressibility in systems with lattice translation symmetry. Critical drag therefore seems to be the only way (other than through irrelevant perturbations breaking the emergent symmetry, that disappear at the renormalization group fixed point) to get nonzero resistivity in such systems. Finally, we present a very simple and concrete model -- the "Quantum Lifshitz Model" -- that illustrates the critical drag mechanism as well as the other considerations of the paper.

Synthesis and characterization of ZnO nanoparticles in n-hexanol solution

Zinc oxide (ZnO) nanoparticles were synthesized by solution chemistry method with n-hexanol as solvent. The synthesized ZnO nanoparticles were characterized by Ultraviolet–visible spectroscopy, transmission electron microscope and X-ray powder diffraction, and the growth kinetics was studied by Lifshitz, Slyozov and Wagner model. The effects of temperature, the addition of deionized water and the concentration of zinc acetate dihydrate on the synthesis of ZnO nanoparticles were investigated. The results show that the nucleation and growth of ZnO nanoparticles were promoted by the addition of small amount of water, and the size of synthesized ZnO nanoparticles could be controlled by changing the amount of water addition and the concentration of zinc acetate dihydrate.

Ultrafast Carrier-Lattice Interactions and Interlayer Modulations of Bi2Se3 by X-ray Free-Electron Laser Diffraction.

As a 3D topological insulator, bismuth selenide (Bi2Se3) has potential applications for electrically and optically controllable magnetic and optoelectronic devices. Understanding the coupling with its topological phase requires studying the interactions of carriers with the lattice on time scales down to the subpicosecond regime. Here, we investigate the ultrafast carrier-induced lattice contractions and interlayer modulations in Bi2Se3 thin films by time-resolved diffraction using an X-ray free-electron laser. The lattice contraction depends on the carrier concentration and is followed by an interlayer expansion accompanied by oscillations. Using density functional theory and the Lifshitz model, the initial contraction can be explained by van der Waals force modulation of the confined free carrier layers. Our theoretical calculations suggest that the band inversion, related to a topological phase transition, is modulated by the expansion of the interlayer distance. These results provide insights into the topological phase control by light-induced structural change on ultrafast time scales.

Crystal Structure-Free Method for Dielectric and Polarizability Characterization of Crystalline Materials at Terahertz Frequencies.

Terahertz (THz) time-domain spectroscopy provides a direct and nondestructive method for measuring the dielectric properties of materials directly from the phase delay of coherent electromagnetic radiation propagating through the sample. In cases when crystals are embedded within an inert polymeric pellet, the Landau, Lifshitz, and Looyenga (LLL) effective medium model can be used to extract the intrinsic dielectric constant of the crystalline sample. Subsequently, polarizability can be obtained from the Clausius-Mossotti (CM) relationship. Knowledge of the crystal structure density is required for an analytical solution to the LLL and CM relationships. A novel crystal structure-free graphical method is presented as a way to estimate both dielectric constants and polarizability values for the situation when the crystal structure density is unknown, and the crystals are embedded within a pellet composed of a non-porous polymer. The utility of this crystal structure-free method is demonstrated by analyzing THz time-domain spectra collected for a set of amino acids (L-alanine, L-threonine, and L-glutamine) embedded within pellets composed of polytetrafluoroethylene. Crystal structures are known for each amino acid, thereby enabling a direct comparison of results using the analytical solution and the proposed crystal structure-free graphical method. For each amino acid, the intrinsic dielectric constant is extracted through the LLL effective medium model without using information of their crystal structure densities. THz polarizabilities are then calculated with the CM relationship by using the determined intrinsic dielectric constant for each amino acid coupled with its crystal density as determined graphically. Comparison between the analytical and graphical solutions reveal relative differences between dielectric constants of 3.7, 5.1, and 13.6% for threonine, alanine, and glutamine, respectively, and relative differences between polarizability of 0.6, 0.9, and 5.4%, respectively. These values were determined over the 10-20 cm-1 THz frequency range. The proposed method requires no prior knowledge of crystal structure information.

Entanglement entropy of excited states in the quantum Lifshitz model

In this work we calculate the entanglement entropy of certain excited states of the quantum Lifshitz model (QLM). The QLM is a 2 + 1-dimensional bosonic quantum field theory with an anisotropic scaling symmetry between space and time that belongs to the universality class of the quantum dimer model and its generalizations. The states we consider are constructed by exciting the eigenmodes of the Laplace–Beltrami operator on the spatial manifold of the model. We perform a replica calculation and find that, whenever a simple assumption is satisfied, the bipartite entanglement entropy of any such excited state can be evaluated analytically. We show that the assumption is satisfied for all excited states on the rectangle and for almost all excited states on the sphere and provide explicit examples in both geometries. We find that the excited state entanglement entropy obeys an area law and is related to the entanglement entropy of the ground state by two universal constants. We observe a logarithmic dependence on the excitation number when all excitations are put onto the same eigenmode.